1. The problem statement, all variables and given/known data A bacteria culture initially contanis 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420. a. Find an expression for the number of bacteria after t hours. b. find the number of bacteria after 3 hours c. find the rate of growth after 3 hours. d. when will population reach 10,000? 2. Relevant equations This is done in section of the book of expontial growth and decay, so equations dP/dt = kP P(t) = P0 e^kt 3. The attempt at a solutionI I managed to solve it, but I had some questions about the exponentials. For part a, I got P'(t) = 100P, and if P'(1) = 420, P = 4.2 However, for c., I had to end up taking the differential of P(t) to get P'(t) = 143.5e^1.435t Ultimately, at t = 1, these give the same answer. But I don't understand how I'm supposed to know when to get either equation... Would my answer for C have been incorrect for A?